38 ideas
6602 | Philosophy is like a statue which is worshipped but never advances [Bacon] |
12124 | Metaphysics is the best knowledge, because it is the simplest [Bacon] |
12123 | Natural history supports physical knowledge, which supports metaphysical knowledge [Bacon] |
12119 | Physics studies transitory matter; metaphysics what is abstracted and necessary [Bacon] |
12120 | Physics is of material and efficient causes, metaphysics of formal and final causes [Bacon] |
10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
10763 | Completeness and compactness together give axiomatizability [Tharp] |
10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
16639 | Only individual bodies exist [Bacon] |
594 | Speusippus suggested underlying principles for every substance, and ended with a huge list [Speussipus, by Aristotle] |
16625 | In hylomorphism all the explanation of actions is in the form, and the matter doesn't do anything [Bacon] |
16033 | There are only individual bodies containing law-based powers, and the Forms are these laws [Bacon] |
16724 | The senses deceive, but also show their own errors [Bacon] |
12121 | We don't assume there is no land, because we can only see sea [Bacon] |
3648 | Empiricists are collecting ants; rationalists are spinning spiders; and bees do both [Bacon] |
12117 | Science moves up and down between inventions of causes, and experiments [Bacon] |
6603 | Nature is revealed when we put it under pressure rather than observe it [Bacon] |
21950 | Science must clear away the idols of the mind if they are ever going to find the truth [Bacon] |
12127 | Many different theories will fit the observed facts [Bacon] |
12126 | People love (unfortunately) extreme generality, rather than particular knowledge [Bacon] |
12125 | Teleological accounts are fine in metaphysics, but they stop us from searching for the causes [Bacon] |
16624 | Stripped and passive matter is just a human invention [Bacon] |
12118 | Essences are part of first philosophy, but as part of nature, not part of logic [Bacon] |
7399 | Even without religion, there are many guides to morality [Bacon] |
2632 | Speusippus said things were governed by some animal force rather than the gods [Speussipus, by Cicero] |